al physic - Ans.fyi 參考答案

al physic

☆ 天與空 ★ ◤

2009-09-28 3:37 am

Two railway lines cross each other at right angles. Train A travelling at 40 km h^-1 crosses the junction at 6p.m. Train B moving along the other line at 25 km h^-1 crosses the junction at midnight. Find the time when they were nearest to each other.

thanks

回答 (1)

天同

2009-09-30 4:35 am

✔ 最佳答案

Let train A travels in the +ve y direction and train B travels along the +ve X direction.
That is, train A passes through the orign at 6:00pm and train B passes through the origin at midnight. The distance between them at 6:00pm is 25 x 6 km = 150 km
By using vector (velocity) diagram, the velocity of train A relative to B is of magnitude = square-root[40^2 + 25^2] km/h = 47.17 km/h, and at direction arc-tan(40/25) = 58 degrees with the -ve X-axis.
Hence, the distance that train A would travel before the closest distance of approach = 150.cos(58) km = 79.49 km
Hence, time required = 79.49/47.17 hrs. = 1.685 hrs = 1 hr. 45 min.
Therefore, the time of closest appraoch = 7:45 pm

👍 0 👎 0